Question 24.4: Although it served our purposes for illustrating the shootin...

Although it served our purposes for illustrating the shooting method, Eq. (24.6) was not a completely realistic model for a heated rod. For one  thing, such a rod would lose heat by mechanisms such as radiation that are nonlinear.
0=\frac{d^2 T}{d x^2}+h^{\prime}\left(T_{\infty}-T\right)        (24.6)
Suppose that the following nonlinear ODE is used to simulate the  temperature of the heated rod:
0=\frac{d^2 T}{d x^2}+h^{\prime}\left(T_{\infty}-T\right)+\sigma^{\prime \prime}\left(T_{\infty}^4-T^4\right)
where σ′ = a bulk heat-transfer parameter reflecting the relative impacts of radiation and conduction = 2.7 × 10^{−9}  K^{−3}  m^{−2}. This equation can serve to illustrate how the shooting method is used to solve a two-point nonlinear boundary-value problem. The remaining problem conditions are as specified in Example 24.2: L = 10  m,  h^′ = 0.05  m^{−2},  T_∞ = 200  K,  T (0) = 300  K, \text{ and } T (10) = 400  K.